Mister Exam
Factor x^2+6*x*y+y^2 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$y^{2} + \left(x^{2} + 6 x y\right)$$
Let us write down the identical expression
$$y^{2} + \left(x^{2} + 6 x y\right) = - 8 y^{2} + \left(x^{2} + 6 x y + 9 y^{2}\right)$$
or
$$y^{2} + \left(x^{2} + 6 x y\right) = - 8 y^{2} + \left(x + 3 y\right)^{2}$$
in the view of the product
$$\left(- \sqrt{8} y + \left(x + 3 y\right)\right) \left(\sqrt{8} y + \left(x + 3 y\right)\right)$$
$$\left(- 2 \sqrt{2} y + \left(x + 3 y\right)\right) \left(2 \sqrt{2} y + \left(x + 3 y\right)\right)$$
$$\left(x + y \left(3 - 2 \sqrt{2}\right)\right) \left(x + y \left(2 \sqrt{2} + 3\right)\right)$$
$$\left(x + y \left(3 - 2 \sqrt{2}\right)\right) \left(x + y \left(2 \sqrt{2} + 3\right)\right)$$
$$y^{2} + \left(x^{2} + 6 x y\right)$$
Let us write down the identical expression
$$y^{2} + \left(x^{2} + 6 x y\right) = - 8 y^{2} + \left(x^{2} + 6 x y + 9 y^{2}\right)$$
or
$$y^{2} + \left(x^{2} + 6 x y\right) = - 8 y^{2} + \left(x + 3 y\right)^{2}$$
in the view of the product
$$\left(- \sqrt{8} y + \left(x + 3 y\right)\right) \left(\sqrt{8} y + \left(x + 3 y\right)\right)$$
$$\left(- 2 \sqrt{2} y + \left(x + 3 y\right)\right) \left(2 \sqrt{2} y + \left(x + 3 y\right)\right)$$
$$\left(x + y \left(3 - 2 \sqrt{2}\right)\right) \left(x + y \left(2 \sqrt{2} + 3\right)\right)$$
$$\left(x + y \left(3 - 2 \sqrt{2}\right)\right) \left(x + y \left(2 \sqrt{2} + 3\right)\right)$$
Factorization
[src]
/ / ___\\ / / ___\\ \x - y*\-3 + 2*\/ 2 //*\x + y*\3 + 2*\/ 2 //
$$\left(x - y \left(-3 + 2 \sqrt{2}\right)\right) \left(x + y \left(2 \sqrt{2} + 3\right)\right)$$
(x - y*(-3 + 2*sqrt(2)))*(x + y*(3 + 2*sqrt(2)))
Combining rational expressions
[src]
2 y + x*(x + 6*y)
$$x \left(x + 6 y\right) + y^{2}$$
y^2 + x*(x + 6*y)